Roger Covenant is the son of Thomas and Joan Covenant. He is initially mentioned in The First Chronicles of Thomas Covenant, where it is revealed that Joan, his mother, has removed him as an infant from his father's home, for fear of the latter's leprosy. However, it isn't until The Third Chronicles that Roger actually comes onto stage, now a twenty-something adult.
Roger most resembles his father, Thomas, although obviously a younger version (duh!). On closer inspection though, it can be seen that Roger has none of his father's severity of expression and overall air of gaunt and tortured asceticism - plus obviously, pieces don't keep dropping off of him. Roger has an unpleasant, softer look about him, as if he's led a somewhat dissolute lifestyle - indulging a little too much on Budweiser and junk food.
Speaking of resembling his father, in Fatal Revenant, with the help of a little malign sorcery, Roger manages to transform himself into a dead ringer of his dad. So much so that he entirely dupes Linden (not that she's ever the brightest lightbulb in anyone's box).
Roger is pretty much an utterly selfish piece of crap. His sole interest is himself... so much so that, via a staggeringly unwise bargain with Lord Foul (geez, the clue's in the name, dumbass... you seriously expect him to deliver?) he expects to be turned into a god and achieve immortality. Not the sharpest knife in the kitchen drawer, then.
Roger doesn't give a rat's ass about either of his parents, having ignored his father all his life and having incarcerated his mother in the local funny farm. He is however very attracted to items of power, which clearly demonstrates his ill-concealed megalomania.
Roger also acts somewhat immature for his age, having an unfortunate habit of shouting mild insults at the top of his lungs at the most inappropriate of moments, e.g. his yelling of "Sucker!" just as he mischievously punches his fist through the Harrow's back. If this isn't a mild form of Tourette's Syndrome, then what a naughty little murderous scamp he is, huh?
As well as his oh so foolish alliance with Lord Foul (see above), Roger also decides to buddy on up with Kastenessen the insane Elohim who's meant to be safeguarding the earth against the skurj. This seems suspiciously quite a bit more than your average bromance, since Roger and Kastenessen don't exchange rings. Oh no, they go a whole heap further and actually swap hands. Yes, Kastenessen, who by now has become part-skurj and entirely given up on his job as some glorified security guard, uses his mad arcane theurgies to graft his own flaming right hand formed of molten lava onto Roger while fusing the human counterpart onto himself. Roger is of course delighted with this added level of power that he now possesses, but one might well think that from then on in, he'd have to always very carefully remember which hand to pick his nose with.
As an aside, the above incident gives rise to the best of the "Covenant walks into a bar" jokes, which goes thus:
Roger Covenant walks into a bar. Upon seeing him, Kastenessen turns round to the other clientèle and shouts "Hey everyone! it's Roger Covenant! Let's give him a warm hand!"
For some unknown reason, Roger seems to be venerated by the entire race of cavewights. He is often to be found riding one of these (errr... we're not sure exactly what this is intended to mean either) as he drives these cannonfodder on into yet another fruitless attack on the good guys. Roger, being an arrant coward, makes sure he stays well in the rear (geez but these innuendos are getting worse) so that he can beat a hasty retreat as soon as the battle starts going against his army of fell creatures - as it invariably does.
Roger finally comes to a sticky end - well, a wet and gelatinous end, to be precise - when Lord Foul mashes him into the ground of Kiril Threndor with a giant fist. However, before he ends up looking like roadkill, Roger does drive Loric Vilesilencer's krill into the shadowy form of the Despiser, in some eldritch way pinning him there in the cavern. It may be that he, looking into the face of his own imminent death, does this as a final act of selfless heroism - but it's actually far more likely that he's really pissed at Lord Foul for having reneged (yet again... do these people never learn?) on his promise to make Roger a god.